Evaluation method for influence of intermediate frequency error of laser element on light beam quality

Abstract

The invention discloses a method for evaluating the influence of an intermediate frequency error of a laser element on light beam quality, and relates to the technical field of optical processing, and the method comprises the following steps: obtaining the surface shape of the surface of an optical element, and carrying out the two-dimensional Fourier transformation of the surface shape of the surface of the optical element; performing spectral analysis on the converted surface shape vector height of the optical element corresponding to the power spectral density to obtain a medium-high frequency periodic order item; selecting a representation function based on the screening result, and selecting a corresponding function secondary level according to the distribution condition of the periodic ripples in the coordinate system to construct a function surface; and fitting the constructed function surface with the original surface shape to obtain coefficients of all levels of the representation function, and completing representation of errors of different frequency bands on the optical element in different spatial periods through the coefficients. The characterization method solves the problems that an existing medium-high frequency band error characterization mode cannot be separated according to different spatial frequencies and amplitudes and cannot research the influence of the different spatial frequencies and amplitudes, and the guiding capacity for optical processing is limited.

Description

Technical Field

[0001] The invention relates to the technical field of optical processing, and in particular to a method for evaluating the influence of intermediate frequency error of a laser element on beam quality. Background Art

[0002] In the process of manufacturing optical components, manufacturing errors are inevitable in engineering, resulting in inconsistency between the actual surface shape and the ideal surface shape. This part of the error can be divided into low-frequency error and medium-high frequency error according to the size of the spatial frequency. Among them, low-frequency error is mainly reflected in the surface shape error caused by inaccurate processing, and medium-high frequency error is caused by different process methods, periodic processing paths, ringing effects, etc. in the processing process. In the strong light system, the frequency band error will cause the degradation of the beam quality, which is mainly reflected in the focusing degree of the beam and the uniformity of the output light spot. What's more, the beam may be focused outside the designed optical path and damage the optical component. In order to qualitatively study the impact of different frequency band errors on the beam quality and specifically remove the frequency band errors of specific spatial frequencies, it is necessary to mathematically characterize the frequency band errors on the surface of optical components so that it can accurately describe the surface shape while facilitating the study of its impact on the beam quality.

[0003] There are relatively rich studies on existing low-frequency error characterization methods such as Zernike polynomials, Legendre polynomials, etc. and their impact on optical systems. However, for research on how to characterize errors in mid- and high-frequency bands, existing methods such as statistical characteristics or power spectral density curves cannot separate frequency band errors according to different spatial frequencies and amplitudes and study their impacts, and their ability to guide optical processing is limited. Summary of the invention

[0004] The present invention aims to solve the deficiencies of the prior art and to provide a method for evaluating the influence of the intermediate frequency error of a laser element on the beam quality. This scheme is adopted to solve the problem that the existing method for characterizing errors in the intermediate and high frequency bands cannot separate them according to different spatial frequencies and amplitudes and study their influence, and has limited guiding ability for optical processing.

[0005] The present invention is achieved through the following technical solutions:

[0006] A method for evaluating the influence of intermediate frequency error of a laser element on beam quality comprises the following steps:

[0007] Acquiring the surface shape of the optical element, and performing a two-dimensional Fourier transform on the surface shape of the optical element;

[0008] Performing spectrum analysis on the power spectrum density corresponding to the transformed surface vector height of the optical element, selecting the corresponding spatial frequencies with sufficiently high frequency domain amplitudes as dense frequencies, and obtaining medium and high frequency periodic order terms;

[0009] Based on the screening results, select the characterization function, and according to the distribution of the periodic ripples in the coordinate system, select the corresponding function secondary to construct the function surface;

[0010] The constructed function surface is fitted with the original surface shape to obtain the coefficients of each level of the characterization function, and the coefficients are used to complete the characterization of errors in different frequency bands of the spatial period on the optical element.

[0011] A further solution is to perform spectrum analysis on the power spectrum density corresponding to the transformed surface vector height of the optical element, select the corresponding spatial frequencies with sufficiently high frequency domain amplitude as dense frequencies, and obtain the medium and high frequency periodic order terms. The specific steps include:

[0012] filtering the frequency domain representing spatial frequencies exceeding a first threshold by low-pass filtering;

[0013] Then, the remaining part after filtering is screened, and the part with an amplitude greater than the second threshold is screened out as the frequency domain correspondence of the periodic ripples mainly existing in the original surface shape, so as to obtain the relatively dense medium and high frequency periods on the surface shape of the optical element.

[0014] In a further embodiment, the first threshold is 20 mm.

[0015] A further solution is to use Zernike polynomials or Legendre polynomials in combination with Fourier series as a complete function to characterize the surface shape of the optical element.

[0016] In a further solution, the distribution of the periodic ripples in the coordinate system includes:

[0017] The periodic ripples are distributed along the x and y directions in a Cartesian coordinate system, and / or along the radial and angular directions in a polar coordinate system.

[0018] In a further solution, when the periodic ripples are distributed along the x and y directions in the Cartesian coordinate system, the Fourier series is:

[0019]

[0020] Where: F is the Fourier series function; c is the coefficient of the corresponding order term; M, N are the number of sampling points in the x and y directions respectively; Lx, Ly are the surface lengths in the x and y directions respectively; m, n represent the corresponding order.

[0021] In a further solution, when the periodic ripples are distributed along the x and y directions in a Cartesian coordinate system, the periods in the x and y directions are:

[0022]

[0023] In a further solution, when the periodic ripples are distributed in radial and angular directions in polar coordinates, the Fourier series is:

[0024]

[0025] In a further solution, when the periodic ripples are distributed in radial and angular directions under polar coordinates, the periods in radial and angular directions are:

[0026]

[0027] A further solution is to fit the constructed function surface to the original surface shape by the least square method.

[0028] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0029] 1. The present invention provides a method for evaluating the influence of the intermediate frequency error of a laser element on the beam quality. The method can introduce direct influencing factors in optical processing such as different periods, different amplitudes and different processing methods of the frequency band error as variables into the optical element surface characterization. Characterization methods such as relative power spectral density (PSD), point spread function (PSF), and optical transfer function (MTF) are more direct and specific in the use of influencing factors, which is convenient for subsequent research and guidance of processing work. On the basis of this method, the influence of the period, amplitude and processing method of the frequency band error on the system beam quality can be studied.

[0030] 2. The present invention provides a method for evaluating the influence of the intermediate frequency error of a laser element on the beam quality. The beam quality is analyzed by comparing the characterization results of a single optical element using this method with the characterization results of each element of the system. For example, a diffraction calculation is performed to obtain a diffraction spot, and the standard deviation of the spot is calculated as an evaluation standard for near-field uniformity. The fitting result is compared with the spot characteristics of the actual optical element. After verifying that they are basically consistent, it is considered that this characterization method is accurate and feasible. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and should not be regarded as limiting the scope. For those of ordinary skill in the art, other relevant drawings can be obtained based on these drawings without creative work. In the drawings:

[0032] Figure 1 A flow chart of the steps of the characterization method provided by the present invention;

[0033] Figure 2 The cylindrical original graphic in Embodiment 2 provided by the present invention;

[0034] Figure 3 The cylindrical dense frequency screening diagram in Example 2 provided by the present invention;

[0035] Figure 4 The cylindrical fitting surface shape in Example 2 provided by the present invention;

[0036] Figure 5 The original surface shape of the cone surface in Example 3 provided by the present invention;

[0037] Figure 6 The fitting surface shape in embodiment 3 provided by the present invention;

[0038] Figure 7 The original surface shape of the aspherical cylinder along the angular and radial directions of the intermediate frequency period in Example 4 provided by the present invention;

[0039] Figure 8 The intermediate frequency period in Example 4 provided by the present invention is the fitting surface shape of the aspherical cylinder along the angular and radial directions. DETAILED DESCRIPTION

[0040] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with embodiments and drawings. The exemplary embodiments of the present invention and their description are only used to explain the present invention and are not intended to limit the present invention.

[0041] Embodiment 1:

[0042] This embodiment 1 provides a method for evaluating the effect of the intermediate frequency error of a laser element on the beam quality. Figure 1 As shown, the specific steps include:

[0043] First, the surface shape of the optical element is obtained, and the detection result of the surface shape of the optical element is subjected to a two-dimensional Fourier transform; other available methods can also be used to perform Fourier transform to obtain a vector height distribution spectrum.

[0044] The spectrum of the optical element surface vector height is then processed and analyzed. A low-pass filter is first performed to filter out the frequency domain part representing a spatial frequency exceeding 20 mm, and the remaining part is screened to select the part with a relatively large amplitude as the frequency domain correspondence of the periodic ripples that mainly exist in the original surface shape, thereby obtaining the relatively dense medium and high frequency periods on the optical element surface shape.

[0045] After obtaining the relatively densely distributed medium and high frequency periods on the surface of the optical element, the surface of the optical element is characterized by using Zernike polynomials or Legendre polynomials combined with Fourier series as a complete function, where the first 37 items of the Zernike polynomials are commonly used and have sufficient characterization significance for the low-frequency surface. If the rectangular area is analyzed, the first 15 items of the Legendre polynomials are selected in the same way. Of course, other low-frequency characterization methods can also be used to replace Zernike polynomials or Legendre polynomials, such as Chebyshev polynomials.

[0046] As for the choice of the number of terms in the Fourier series, due to different optical processing methods, the periodic ripples may be distributed along the x and y directions in the Cartesian coordinate system or along the radial and angular directions in the polar coordinate system. In response to this situation, this paper proposes different forms of Fourier series.

[0047] If the ripples are distributed along the x and y directions, use the Fourier series:

[0048]

[0049] The different numbers of terms in the Fourier series, that is, different m, n, establish an obvious connection with different spatial periods. The periods in the x and y directions are:

[0050]

[0051] When the ripples are distributed along the radial and angular directions, the Fourier series is used:

[0052]

[0053] The period in the radial angle upward is:

[0054]

[0055] After completing the selection and construction of the number of terms of the surface characterization function, the constructed function surface is fitted with the original surface shape by the least square method to obtain the coefficients of each number, which represent the amplitude of the frequency band part on the surface shape, thereby completing the characterization of the errors of different frequency bands in the spatial period on the optical element. Of course, other fitting function methods can also be used to obtain the coefficients of the characterization function.

[0056] After obtaining the coefficients of each level of the characterization function, the beam quality of the characterization function surface and the original surface under the same conditions can be compared to verify the accuracy of the characterization function, and the impact of different influencing factors on the beam quality can be predicted based on the characterization function.

[0057] The above scheme provides a method for evaluating the influence of the intermediate frequency error of a laser element on the beam quality. The direct influencing factors in optical processing such as different periods, different amplitudes and different processing methods of the frequency band error can be introduced as variables into the optical element surface characterization. Characterization methods such as relative power spectral density (PSD), point spread function (PSF), optical transfer function (MTF) are more direct and specific in the use of influencing factors, which is convenient for subsequent research and guidance of processing work. On the basis of this method, the influence of the period, amplitude and processing method of the frequency band error on the system beam quality can be studied. The beam quality analysis can also be performed by comparing the characterization results of a single optical element using this method with the characterization results of each element of the system, such as performing diffraction calculations to obtain diffraction spots, calculating the standard deviation of the spots as the evaluation standard for near-field uniformity, comparing the fitting results with the spot characteristics of the actual optical element, and verifying that they are basically consistent. It is believed that this characterization method is accurate and feasible.

[0058] Embodiment 2:

[0059] This embodiment 2 provides an implementation case based on embodiment 1, such as Figure 2-Figure 4 shown.

[0060] The following uses a cylindrical mirror as an example. Figure 2 The target cylindrical surface shape to be fitted:

[0061] The original data is Fourier transformed, and the main density of the composite intermediate frequency periodic ripples in the x and y directions is obtained through frequency domain analysis. Figure 3 shown.

[0062] The fitting function is formed by using the first 15 Legendre polynomials and the Fourier series corresponding to the selected dense frequency. The fitting result is obtained by fitting the original surface shape using the least squares method. Figure 4 shown.

[0063] By calculating the root mean square of the difference between the fitted surface shape and the original surface shape, the surface modeling deviation RMS = 0.009117 <λ / 50 (λ = 632.8nm) is obtained, which meets the requirements of modeling analysis and characterization.

[0064] Embodiment 3:

[0065] This embodiment 3 provides another implementation case based on embodiment 1, such as Figure 5-Figure 6 shown.

[0066] For other typical optical elements such as conical mirrors, the same characterization idea is used to replace the orthogonal Legendre polynomials in the rectangular domain with the orthogonal Zernike polynomials in the circular domain. The first 37 Zernike polynomials and the Fourier series terms corresponding to the dense frequencies screened out after the Fourier transform of the original surface shape and the frequency domain analysis are used to form a fitting function for least squares fitting. The results are as follows Figure 6 shown.

[0067] By calculating the root mean square of the difference between the fitted surface shape and the original surface shape, the surface modeling deviation RMS=0.014539<λ / 20 is obtained, which meets the requirements of modeling analysis and characterization.

[0068] Embodiment 4:

[0069] This embodiment 4 provides another implementation case based on embodiment 1, such as Figure 7-Figure 8 shown.

[0070] For periodic ripples, the direction is not along the x and y directions but along the radial and angular directions. In this case, the Fourier series form needs to be adjusted to polar coordinates. According to this Fourier series form, the first 37 Zernike polynomials and the Fourier series terms corresponding to the dense frequencies screened out after the original surface shape is Fourier transformed and the frequency domain analysis are performed to form a fitting function for least squares fitting. The result is as follows Figure 8 shown.

[0071] By calculating the root mean square of the difference between the fitted surface shape and the original surface shape, the surface modeling deviation RMS=0.009321<λ / 50 is obtained, which meets the requirements of modeling analysis and characterization.

[0072] Embodiment 5:

[0073] In some exemplary embodiments, the present embodiment further provides a device for characterizing the frequency band error on the surface of an optical element and its influence on the beam quality, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, a minimum technical solution for a method for characterizing the frequency band error on the surface of an optical element and its influence on the beam quality is implemented as in Example 1 to achieve the purpose of "solving the problem that the existing method for characterizing medium and high frequency band errors cannot separate them according to different spatial frequencies and amplitudes and study their influence, and has limited guidance ability for optical processing".

[0074] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0075] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0076] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0077] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0078] A person of ordinary skill in the art can understand that all or part of the steps in realizing the above-mentioned facts and methods can be completed by instructing the relevant hardware through a program, and the program involved or the program described can be stored in a computer-readable storage medium. When the program is executed, it includes the following steps: At this time, the corresponding method steps are derived, and the storage medium can be ROM / RAM, a disk, an optical disk, etc.

[0079] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for evaluating the effect of laser element intermediate frequency error on beam quality, characterized in that: The following steps are involved: Acquiring the surface shape of the optical element, and performing a two-dimensional Fourier transform on the surface shape of the optical element; Performing spectrum analysis on the power spectrum density corresponding to the transformed surface vector height of the optical element, selecting the corresponding spatial frequencies with sufficiently high frequency domain amplitudes as dense frequencies, and obtaining medium and high frequency periodic order terms; Based on the screening results, select the characterization function, and according to the distribution of the periodic ripples in the coordinate system, select the corresponding function secondary to construct the function surface; The constructed function surface is fitted with the original surface shape to obtain the coefficients of each level of the characterization function, and the coefficients are used to complete the characterization of errors in different frequency bands of the spatial period on the optical element.

2. The method for evaluating the effect of intermediate frequency error of a laser element on beam quality according to claim 1, characterized in that: The specific steps of performing spectrum analysis on the power spectrum density corresponding to the transformed surface vector height of the optical element, selecting the corresponding spatial frequencies with sufficiently high frequency domain amplitude as dense frequencies, and obtaining the medium and high frequency periodic order terms include: filtering the frequency domain representing spatial frequencies exceeding a first threshold by low-pass filtering; Then, the remaining part after filtering is screened, and the part with an amplitude greater than the second threshold is screened out as the frequency domain correspondence of the periodic ripples mainly existing in the original surface shape, so as to obtain the relatively dense medium and high frequency periods on the surface shape of the optical element.

3. The method for evaluating the effect of intermediate frequency error of a laser element on beam quality according to claim 2, characterized in that: The first threshold is 20 mm.

4. The method for evaluating the effect of intermediate frequency error of a laser element on beam quality according to claim 1, characterized in that: The surface shape of optical components is characterized by combining Zernike polynomials or Legendre polynomials with Fourier series as a complete function.

5. The method for evaluating the effect of intermediate frequency error of a laser element on beam quality according to claim 4, characterized in that: The distribution of the periodic ripples in the coordinate system includes: The periodic ripples are distributed along the x and y directions in a Cartesian coordinate system, and / or along the radial and angular directions in a polar coordinate system.

6. The method for evaluating the effect of intermediate frequency error of a laser element on beam quality according to claim 5, characterized in that: When the periodic ripples are distributed along the x and y directions in the Cartesian coordinate system, the Fourier series is: Where: F is the Fourier series function; c is the coefficient of the corresponding order term; M, N are the number of sampling points in the x and y directions respectively; Lx, Ly are the surface lengths in the x and y directions respectively; m, n represent the corresponding order.

7. The method for evaluating the effect of intermediate frequency error of a laser element on beam quality according to claim 6, characterized in that: When the periodic ripples are distributed along the x and y directions in the Cartesian coordinate system, the periods in the x and y directions are:

8. The method for evaluating the effect of intermediate frequency error of a laser element on beam quality according to claim 5, characterized in that: When the periodic ripples are distributed in radial and angular directions in polar coordinates, the Fourier series is:

9. The method for evaluating the effect of intermediate frequency error of a laser element on beam quality according to claim 8, characterized in that: When the periodic ripples are distributed in the radial and angular directions under polar coordinates, the periods in the radial and angular directions are:

10. The method for evaluating the effect of intermediate frequency error of a laser element on beam quality according to any one of claims 1 to 9, characterized in that: The constructed function surface is fitted to the original surface shape by the least squares method.

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